Clashes resumed today after a short period of calm overnight in the central Mansura district, a stronghold of jihadists.
Warplanes and Apache helicopters from a Saudi-led coalition have carried out air strikes in support of security forces, security sources said.
"At least 17 al-Qaeda fighters and two policemen have been killed since yesterday," a security official told AFP, adding that most of the jihadists were killed in air raids.
The police said in a statement that fighting against the "armed terrorist gangs in Mansura will continue to ensure the safety of residents" in Yemen's main southern city.
Al-Qaeda and the Islamic State group have taken advantage of the conflict between Iran-backed Huthi insurgents and pro-government forces to reinforce their presence in the south, including in Aden.
More than 6,100 people have died -- half of them civilians -- since the coalition launched air strikes against the Shiite rebels and their allies in March 2015, according to the UN.